In a group of $65$ people,$40$ like cricket and $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Let $S = \{(x, y, z) : x, y, z \in \mathbb{Z}, x + 2y + 3z = 42, x, y, z \geq 0\}$. Find the number of elements in $S$.

Let $S = \{1, 2, 3, \ldots, 40\}$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by $5$. What is the maximum number of elements possible in $A$?

The probability of choosing at random a number that is divisible by $6$ or $8$ from among $1$ to $90$ is equal to

In a certain town,$25\%$ of families own a phone,$15\%$ own a car,and $65\%$ of families own neither a phone nor a car. If $2000$ families own both a car and a phone,consider the following statements:
$1$. $10\%$ of families own both a car and a phone.
$2$. $35\%$ of families own either a car or a phone.
$3$. $40,000$ families live in the town.
Which of the above statements are correct?

In a certain town,$65\%$ of families own cell phones,$15000$ families own scooters,and $15\%$ of families own both. Given that every family owns at least one of the two,the total number of families in the town is: